Evaluation of the power law and patchiness regressions with regression diagnostics

We used regression diagnostics to evaluate the robustness of the least-squares regression method for estimating the power law and patchiness regression parameters for 3 data sets of insect counts, specifically for the Bemisia argentifolii Bellows and Perring and the squash bug, Anasa tristis (De Geer). Extreme values in the independent variable, x, and dependent variable, y, were detected with the leverage term, h(i), and standardized residuals, e(s) respectively. The assumption of homogeneity of variances was evaluated with plots of e(s) against x for all regressions, and significant autocorrelations were tested with the Durbin-Watson statistic. For both techniques, we compared least-squares regression results for all data with regressions obtained after outlier data points were removed. We also calculated power law regressions excluding means (m) <2 and variances (s²) <4 to reduce possible bias resulting from small mean densities. Outlier data points did not have a significant effect on the power law regressions, but they had a strong influence on some patchiness regressions. The distribution of standardized residuals of some power law regressions were biased toward positive values for low mean densities, indicating underestimation of variances. Additionally, least-squares regression estimates for m ≤2, s² ≤4 indicated a general increase in slopes for the power law. The distribution of standardized residuals for patchiness regressions indicated strong heteroscedasticity; therefore the assumption of constant variance for y was not fulfilled. Our results show that suitability of least-squares regression assumptions should be considered whenever pest management decisions are based on the power law or patchiness regressions.